Friday 7 June 2013

n-ary therapy

I reckon these two puzzles are probably the closest to puzzling therapy you can find...

I picked up a copy of Thinkfun’s Spin Out via Amazon recently because I reckoned that every puzzle collection needs a copy... based on the Gray code principle, each of the seven dials needs to be in a horizontal position in order to allow the central slider to move out – but since each of the dials interferes with its neighbours you need to follow a series of moves to successively unlock each dial ... except that you’ll find that you need to keep going backwards and forwards ... and in the end it takes 85 moves to get the central slider out... 
Helpfully this version of Spin Out has a short-cut back to the beginning in the form of an opening on the side that lets you insert the central slider in the locked position...neat! the way, if you’re interested – Spin Out was invented by William Keister while working at Bell Labs where a colleague, Frank Gray, had invented a technique for error correction in electronic communications ... which subsequently became known as the Gray Code ... see the link there... :-)

[Jaap Scherphuis’ wonderfully useful website has some great analysis of Spin Out –  - including a recursive formula for working out how many moves are required for this sort of puzzle – L(n) = L(n-1) + 2*L(n-2) + 1, starting with L(1)=1 and L(2)=2 ... which all collapses down to L(n) = INT [2^(n+1) / 3].   ]
The second bit of n-ary therapy comes in the form of Crazy Elephant Dance by Markus Götz. I got this one from Peter Knoppers when I met up with him at Wil’s – Peter sells them as laser-cut wooden kits for a jolly decent price and I spent a couple of hours putting it all together. The bits all go together quite easily and the kits have been designed to ensure that the critical alignment is all taken care of with the help of a bunch of cocktail sticks – clever...
Once it was all together, the first order of business was actually locking the puzzle up – you build the frame and the slider separately and then have to progressively lock the puzzle up. The dials on this puzzle take the shape of cute elephants and the twist here is that whereas Spin Out was binary-based with each dial having two interesting positions (vertical or horizontal), this one has three interesting positions (up, right and down) – a ternary Gray code. With only 5 dials / elephants to contend with, the requirements of the ternary design still provides a reasonably lengthy solution path to free the central slider.
The elephants all start with their trunks in the air and there’s a single turning circle where elephants can be rotated, their neighbours permitting. Once you have all the trunks pointing downwards, the slider will be free.

This one’s not only a fun puzzle to build yourself, but the rhythm of running backwards and forwards through the solution path is definitely therapeutic! 

...and I don’t that I’m the only one who thinks that as it won an honourable mention at the 2005 Nob Yoshigahara Puzzle Design Competition.


  1. Thanks for the tip that Peter is selling Crazy Elephant Dance kits! I've always wanted a copy of that one!

    1. Drop Peter a line - if he doesn't have any lying around, I'm sure he'll cut a set for you ... that's what he did for me... :-) allard

  2. Having seen the elephants at MPP 10.5 I contacted Peter and got his last one! I haven't put it together yet but will do so soon. I've recently been on an N-ary buzz and probably bought 10-12 different puzzles in this group including the awesome 7-ary Kugellager with 4082 moves!

    Yep! Definitely addicted!


  3. Kevin and Allard have you solved the java version over on Markus' website yet? It's a great challenge!

    1. I have now! :-) Thanks for the nudge, Michel!